A demonstration or proof of concept (often done for a client) to prove the product works as sold or to show how a design on paper looks once actually built. May or may not be a waste of time. Used in the special effects industry among many others.

I have a Dog and Pony show for the director this afternoon. He wants to see how the exploding car rig looks on film.

when two or more people or organizations pretend to have a very public grievance with each other in order to create publicity and buzz for their product/service, etc.
Pro wrestling is full of dog and pony act story-lines.

Tito Ortiz made a bunch of rude comments to Ken Shamrock, and Ken lost it and nearly started a fight at the press conference. I know they hate each other, but it's really just a dog and pony show to drum up interest in the fight.